VITEEE 2010 Paper

F(x+2) = 2F(x) - F(x+1)...(i)
Putting x = 0, we get
F(2) = 2F(0) - F(1)
⇒ F(2) = 2(2) - 3{ ∵ F(0) = 2, F(1) = 3 }
⇒ F(2) = 4 - 3
⇒ F(2) = 1
Putting x = 1, in eq. (i), we get
F(3) = 2F(1) - F(2) = 2(3) - 1{∵ F(1) = 3, F(2) = 1}
⇒ F(3) = 5
Putting x = 2, in eq. (i), we get
F(4) = 2F(2) - F(3) = 2(1) - 5{∵ F(2) = 1, F(3) = 5}
⇒ F(4) = -3
Putting x = 3, in eq. (i), we get
F(5) = 2F(3) - F(4) = 2(5) + 3{∵ F(3) = 5, F(4) = -3}
⇒ F(5) = 13